Application of Bezier surfaces to the 3-D inverse geometry problem in continuous casting

Figures & data

Figure 1. (a) Scheme of the 3-D domain and (b) boundary condition types for two side views of the continuous casting problem of aluminium alloy.

Figure 2. Bezier surface with control points (the inverse view).

Table 1. Absolute and relative error locations of the phase change front and the Bezier control point for different measurement errors.

Error of measurements	Absolute error of front location (m)	Relative error of front location (%)	Relative error of Bezier control points local (%)
0.0	0.1405	14.05	1.903
0.2	0.1410	14.10	2.164
0.5	0.1415	14.15	2.376
1.0	0.1422	14.22	2.485

Table 2. Temperature measured and calculated at selected (odd) sensor location.

Sensor number	Simulated measurements^a	Temperature calculated for maximum measurement erros 0.2%	Temperature calculated for maximum measurement errors 1.0%
1	817.6	816.9	817.1
3	813.5	812.9	812.9
5	768.0	769.0	768.4
7	830.6	830.6	830.4
9	808.0	807.9	808.6
11	837.2	837.4	837.4
13	834.7	834.8	835.0
15	827.6	827.7	827.7
Note: ^aTemperature obtained in the direct model which is the basis for the measurement simulation.

Figure 3. Changes of phase change front location for selected iterations (for maximum error 1.0%).